On the existence and uniqueness of solutions to dynamic equations

Authors: BAŞAK KARPUZ

Abstract: In this paper, we prove the well-known Cauchy-Peano theorem for existence of solutions to dynamic equations on time scales. Some simple examples are given to show that there may exist more than a single solution for dynamic initial value problems. Under some certain conditions, it is also shown that there exists only one solution.

Keywords: Cauchy-Peano theorem, Picard-Lidelof theorem, dynamic equations, time scales

Full Text: PDF